PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Polarisation and anisotropic media · Polarisation and anisotropic media
What an Instrument Can See, Ch Polarisation as a statistical object: coherency and Mueller matrices
Problem
An LED emits unpolarised light of irradiance I0=4.0mWmm−2. Suppose we treat unpolarised light as "just a Jones vector whose azimuth spins around too fast to see", and pick the horizontal Jones vector (I0,0) as a stand-in for "the beam at some instant", and then use Malus's law to predict the power transmitted by an ideal polariser set at 60∘ to the horizontal.
((a)) Compute the transmitted irradiance this shortcut predicts.
((b)) Write down the coherency matrix of the actual unpolarised beam, confirm it is Hermitian and positive semi-definite, and find the irradiance an ideal polariser at 60∘ actually transmits.
((c)) Explain why the shortcut agrees with the real beam only at isolated polariser angles, and why the real beam transmits the same irradiance at every polariser angle.